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Refactoring improved adder implementation #359

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Refactoring improved adder implementation #359

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412e5a8
Refactor.
Oct 26, 2020
b36fe9c
Save some operations.
Oct 26, 2020
8e1b491
Apply suggestions from code review
msoeken Nov 5, 2020
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86 changes: 38 additions & 48 deletions Standard/src/Arithmetic/Integer.qs
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Original file line number Diff line number Diff line change
Expand Up @@ -25,15 +25,19 @@ namespace Microsoft.Quantum.Arithmetic {
/// Carry-out qubit, will be xored with the higher bit of the sum.
operation Carry(carryIn: Qubit, summand1: Qubit, summand2: Qubit, carryOut: Qubit)
: Unit is Adj + Ctl {
CCNOT (summand1, summand2, carryOut);
CNOT (summand1, summand2);
CCNOT (carryIn, summand2, carryOut);
CCNOT(summand1, summand2, carryOut);
CNOT(summand1, summand2);
CCNOT(carryIn, summand2, carryOut);
}

/// # Summary
/// Implements a compute carry gate using a temporary logical-AND construction.
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Is this related to figure 1 in this paper (https://arxiv.org/pdf/1709.06648.pdf)? If yes could we link it here?

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This operation is not related to that paper. It has been used in the previous implementation, and only remains in the code, because it has been exposed as public API. It basically computes the majority-of-three function out-of-place into carryOut, but also changes the state of summand2.

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Ok thanks! Is there another reference we can link here?

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/// The input parameters `(carryIn, summand1, summand2, carryOut)` are passed together as a tuple
/// to have a more natural call to `ApplyToEachA` in the calling function.
///
/// # Input
/// ## controls
/// Possible control lines.
/// ## carryIn
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/// Carry-in qubit.
/// ## summand1
Expand All @@ -43,40 +47,20 @@ namespace Microsoft.Quantum.Arithmetic {
/// `summand1` and `summand2`.
/// ## carryOut
/// Carry-out qubit, will be xored with the higher bit of the sum.
internal operation ComputeTemporaryCarry(carryIn: Qubit, summand1: Qubit, summand2: Qubit, carryOut: Qubit)
: Unit is Adj{
CNOT(carryIn, summand2);
CNOT(carryIn, summand1);
ApplyAnd(summand1, summand2, carryOut);
CNOT(carryIn, carryOut);
}

/// # Summary
/// Implements a erase carry gate by uncomputing the logical-AND.
///
/// # Input
/// ## carryIn
/// Carry-in qubit.
/// ## summand1
/// First summand qubit.
/// ## summand2
/// Second summand qubit, is replaced with the lower bit of the sum of
/// `summand1` and `summand2`.
/// ## carryOut
/// Carry-out qubit, will be erased
internal operation EraseTemporaryCarry(carryIn: Qubit, summand1: Qubit, summand2: Qubit, carryOut: Qubit)
: Unit is Adj + Ctl{
body (...){
CNOT (carryIn, carryOut);
(Adjoint ApplyAnd) (summand1, summand2, carryOut);
CNOT (summand1, summand2);
CNOT(carryIn, summand1);
internal operation ApplyRippleCarryAdderDBlock(controls : Qubit[], (carryIn : Qubit, summand1 : Qubit, summand2 : Qubit, carryOut : Qubit))
: Unit is Adj
{
body (...) {
CNOT(carryIn, summand2);
CNOT(carryIn, summand1);
ApplyAnd(summand1, summand2, carryOut);
CNOT(carryIn, carryOut);
}
controlled (controls, ...) {

adjoint (...) {
CNOT (carryIn, carryOut);
(Adjoint ApplyAnd) (summand1, summand2, carryOut);
(Controlled CNOT) (controls, (summand1, summand2));
Adjoint ApplyAnd(summand1, summand2, carryOut);
Controlled CNOT(controls, (summand1, summand2));
CNOT(carryIn, summand1);
CNOT(carryIn, summand2);
}
Expand Down Expand Up @@ -136,32 +120,38 @@ namespace Microsoft.Quantum.Arithmetic {
body (...) {
Controlled RippleCarryAdderD(new Qubit[0], (xs, ys, carry));
}
controlled ( controls, ... ) {
controlled (controls, ... ) {
let nQubits = Length(xs!);

EqualityFactI(
nQubits, Length(ys!),
"Input registers must have the same number of qubits."
);

using (auxRegister = Qubit[nQubits-1]) {
using (auxRegister = Qubit[nQubits - 1]) {
within {
ApplyAnd (xs![0], ys![0], auxRegister[0]);
ApplyAnd(xs![0], ys![0], auxRegister[0]);
ApplyToEachA(
ApplyRippleCarryAdderDBlock(controls, _),
Zipped4(Most(auxRegister), xs![1..nQubits - 2], ys![1..nQubits - 2], Rest(auxRegister))
);
}
apply {
for (idx in 1..(nQubits-2)) {
ComputeTemporaryCarry(auxRegister[idx-1], xs![idx], ys![idx], auxRegister[idx]);
}
// carry out is computed using Carry and Sum since using temporary Logical-AND construction erases the carry bit
(Controlled Carry) (controls, (auxRegister[nQubits-2], xs![nQubits-1], ys![nQubits-1], carry));
(Controlled CNOT) (controls, (xs![nQubits-1], ys![nQubits-1]));
(Controlled Sum) (controls, (auxRegister[nQubits-2], xs![nQubits-1], ys![nQubits-1]));
for (idx in (nQubits-2)..-1..1) {
(Controlled EraseTemporaryCarry) (controls, (auxRegister[idx-1], xs![idx], ys![idx], auxRegister[idx]));
// carry out is computed using a majority-of-three operation
within {
CNOT(Tail(auxRegister), Tail(xs!));
CNOT(Tail(auxRegister), Tail(ys!));
} apply {
Controlled ApplyAnd(controls, (Tail(xs!), Tail(ys!), carry));
Controlled CNOT(controls, (Tail(auxRegister), carry));
}

// final sum
Controlled CNOT(controls, (Tail(auxRegister), Tail(ys!)));
Controlled CNOT(controls, (Tail(xs!), Tail(ys!)));
}
// low bit output computation is simplified since CarryIn is always |0>
(Controlled CNOT) (controls, (xs![0], ys![0]));

Controlled CNOT(controls, (xs![0], ys![0]));
}
}
}
Expand Down